Ideas for Destructive Procrastination

April 24, 2004

#1 Idea: Continuing to blog when you have a PhD qualifying oral exam in 5 days.

Hence, the blog’s going to be on hiatus until Thursday, April 29th or so, when I’ll start tackling some big questions like (1) what a grand centrist compromise between liberals and conservatives might look like and (2) a common sense guide to contemplating interpretations of quantum mechanics without going insane.

If you want to do some background reading on these topics…

************************

(For Topic 1 – On Radical Centrist Reform of Government)

My starting point is the proposal of Matthew Miller, which can be found on his blog and in his book The 2% Solution, which gets its name from the notion that by returning the size of government to 22% of GDP (the average during the Reagan-Bush years) rather than the 20% of GDP now, we could implement a comprehensive domestic policy including universal health care, lifting the working poor out of poverty, comprehensive education reform, and public financing of political campaigns. If all that sounds really lefty, note that the execution of all these ideas is done in ways conservatives should consider “market-friendly” and “freedom-promoting”.

My main contention will be that for a real grand centrist bargain between liberals and conservatives, a bit more is going to have to be on the table. Notably, major tax reform is going to have to be on the table, which is something Miller neglects. (NB: I said tax reform, i.e., changes to make tax law simpler, more enforceable, and less prone to promulgating perverse incentives, and thus make the economy more efficient, which we really can’t afford not to do anymore… not to be confused with tax cuts, which at this point we sadly can’t afford to do anymore). For ideas, consider:

Joel Slemrod and Jon Bakija Taxing Ourselves: A Citizen’s Guide to the Great Debate over Tax Reform, 2nd Edition (Cambridge, MA – MIT Press 2001)

The various works of Dale Jorgenson, Professor of Economics at Harvard on “Efficient Taxation of Income” (e.g., the following… which are listed in order from most to least difficult):

Efficient Taxation of Income, with Kun-Young Yun, (November 15, 2002) [a long, technical journal paper]

.pdf Slides to the Office of Tax Analysis, August 2, 2002. [a technical presentation]

A Smarter Type of Tax, Financial Times, June 19, 2002 [an op-ed piece]

Efficient Taxation of Income, Harvard Magazine, March-April 2003: Volume 105, Number 4. [a bit of Harvard alumni propaganda]

************************

(For Topic 2 – The Fundamental Nature of Reality or The Lack Thereof)

For laypersons:

John Polkinghorne’s stunningly concise and remarkably non-misleading popularization Quantum Mechanics in Oxford University Press’s “Very Short Introduction” series, which is full-text viewable at Amazon.com

For technical readers with positivist proclivities:

Are you the type of guy or gal who thinks the following?

I’ll ascribe objective reality to a system’s wavefunction with respect to a given observable only if when…

1) … I have a single rendition of the system, and…

2) … I don’t have full a priori knowledge of the system’s preparation, yet…

3) … I can still somehow determine what the wavefunction is without changing it in the process

(I impose this final condition since if it’s inevitably changed, how could I know I really had it and my measurement wasn’t a fluke? I want to be able to repeat my measurements to my heart’s content until I satisfy my inner Bayesian conscience—no matter how neurotically exacting it may be.)

Then you probably should take a look at Quantum Measurement of a Single System by Orly Alter and Yoshihsa Yamamoto, which is also full-text viewable at Amazon.com, because it strongly argues that quantum mechanics will never satisfy your criteria for objective reality. The book proves that quantum mechanics as it’s currently known will not allow you to obtain *any* information about a system’s wavefunction without changing the wavefunction *unless* you have full a priori knowledge of a system’s preparation. (For example, say you’re told that a system has been prepared in an definite energy eigenstate, but you don’t know the full Hamiltonian of the system. There’s no way you can determine what the eigenstate from a single copy of the system without changing the state, no matter how slowly—adiabatically–you perform your manipulations. Or, say you’re given a spin and told it has a definite orientation, but you’re not told what it is. There’s no way to determine the orientation of a single spin without changing it unless you already know what axis it lies on.)

For technical readers fond of noumenal notions:

The following is the most straightforward and sensible thing I’ve come across about the “Many Worlds Interpretation” of quantum mechanics (which, in case you haven’t noticed, underlies the joke that gives this blog its name)

Max Tegmark, “The interpretation of quantum mechanics: many worlds or many words?”, Fortschr. Phys. 46, 855-862 [downloadable Postscript file]

(His webpage devoted to Many Worlds http://www.hep.upenn.edu/~max/everett.html is worth a look too.)

For mathematically minded readers who want to codify a logical system that would encompass all possible interpretations of quantum mechanics that do not involve wavefunction collapse:

Does the following sound like a good idea to you?

… quantum mechanics is not about physical systems that exhibit a peculiar and elusive ontology, but rather about physical systems with a non-Boolean property structure. The problem is then how to make sense of a quantum world in which the properties of systems ‘fit together’ in a non-Boolean way.”

How about when it’s expressed technically?

The actual properties in a classical world are selected by a 2-valued homomorphism from a set of alternatives defined by a fixed Boolean algebra — the Boolean algebra of subsets of the phase space of the classical world — representing the same collection of possible properties at all times. The actual properties in a quantum world at time t are selected by a 2-valued homomorphism from a set of alternatives defined by a dynamically evolving non-Boolean sublattice of all subspaces of the Hilbert space of the quantum world. So the actual properties in a classical world evolve in a fixed Boolean possibility space, while the actual properties in a quantum world evolve in a dynamically changing non-Boolean possibility space. Classically, only the actual properties are time-indexed; quantum-mechanically, both the actual properties and the possible properties are time-indexed.

Modulo the usual philosophical worries about modality, there is nothing inherently strange about the notions of possibility or actuality in quantum mechanics. Once we have a precise handle on what is possible and what is actual, and how change proceeds, the rest is calculation. So measurement comes out as a process internal to the theory, on the basis of the dynamics alone, without requiring any privileged status for observers.

If you answered yes to either question, and especially if you answered yes to the latter question, you should really read the book from which they came:

Jeffrey Bub, Interpreting the Quantum World (Cambridge Univ. Press, corrected edition 1999), which, you guessed it, is also full-text viewable at Amazon.com.

[NB: Bub boasts the stunning academic lineage of being a student of physicist David Bohm and philosophers Karl Popper and Imre Lakatos.]

Advertisements

One Response to “Ideas for Destructive Procrastination”

  1. CSTAR Says:

    Let me first say that I’m from the VonNeumann-Mackey tradition (my pseudonym should give that away), although too much of an outlier for anybody to pay any attention. I’m also more of a finitist in the Edward Nelson (of Princeton) sense who in the grand tradition of american academic narow-mindedness has totally discredited himself by being bold enough to embrace a new idea: nonstandard analysis.

    All scientific theories are idealizations, from quantum mechanics to macroeconomics. The catch with any idealizations is that one stretches them too far. This is the “generalized Sorites fallacy”. To make sense of this, I claim one needs nonstandard analysis (I may have to finish here before the ideological police haul me away).


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: